Fractional Lengths in Triangles and Prisms

5 min

Teacher Prep
Setup
Students in groups of 2. 2 minutes of quiet work time, followed by 1 minute of partner discussion. Review the formula for the area of a triangle before students begin.

Narrative

In this Warm-up, students review how to find the area of a triangle given a pair of base-height measurements. The reasoning here prepares students to use division of fractions to solve area problems involving triangles later in the lesson.

Launch

Arrange students in groups of 2. Give students 2 minutes of quiet work time, followed by 1 minute of partner discussion. Before students begin, review the formula for the area of a triangle. Consider displaying a drawing of a triangle with one side labeled as a base and a corresponding height shown and labeled as such. 

Student Task

Find the area of Triangle A in square centimeters.
Show your reasoning.

Triangle labeled A.
A triangle labeled A with a vertical side. One vertex is to the left of the vertical side. A dashed horizontal line is drawn from the first vertex to the vertical side of the triangle and a right angle symbol is indicated. The dashed line and the vertical side are both labeled 4 and one half centimeters.

Sample Response

101810\frac{1}{8} cm2. Sample reasoning: The area of any triangle is A=12⋅\mboxbase⋅\mboxheightA=\frac12\boldcdot \mbox{base}\boldcdot \mbox{height} and 12⋅(412)⋅(412)=1018\frac12\boldcdot \left(4\frac12\right)\boldcdot \left(4\frac12\right)=10\frac18.

Activity Synthesis (Teacher Notes)

Invite a student to share a solution and reasoning. Record it for all to see. Ask if others used alternative ways of reasoning, and invite them to share their approaches (as many as time permits).

If any student wrote the fraction 4124\frac{1}{2} as 4.5 before performing any operations, consider discussing how the calculations are alike and how they are different.

Tell students that they will solve more problems involving the area of triangles in this lesson.

Standards
Addressing
  • 6.G.1·Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • 6.G.A.1·Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • 6.NS.1·Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. <em>For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?</em>
  • 6.NS.A.1·Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. <span>For example, create a story context for <span class="math">\((2/3) \div (3/4)\)</span> and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that <span class="math">\((2/3) \div (3/4) = 8/9\)</span> because <span class="math">\(3/4\)</span> of <span class="math">\(8/9\)</span> is <span class="math">\(2/3\)</span>. (In general, <span class="math">\((a/b) \div (c/d) = ad/bc\)</span>.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? </span>

10 min

20 min